Serves2 (first course)
                    
                
                
                    
                        
                            - Active Time:45 min
- Start to Finish:2 3/4 hr (includes chilling)
 
            
            
                
                
                
    
      
          
          
          
              
              
              
          
          
          
          
          
              
              
              January 2004
            
          
          
      
  
                
                
            
            
            
                If you don’t want to cook a live lobster for this recipe, buy 2/3 pound cooked lobster meat from your seafood shop.
            
            
            
            
            
                
                    
                    
                    
                        
                            
                            
                            
                                
                                    
                                        - 
                                            1
                                            
                                            (1 1/4- to 1 1/2-lb) live lobster
                                            
                                        
- 
                                            2
                                            teaspoons
                                            finely chopped shallot
                                            
                                        
- 
                                            1
                                            tablespoon
                                            fresh lemon juice
                                            
                                        
- 
                                            1/4
                                            teaspoon
                                            table salt
                                            
                                        
- 
                                            2
                                            tablespoons
                                            extra-virgin olive oil
                                            
                                        
- 
                                            1
                                            
                                            pink or ruby-red grapefruit
                                            
                                        
- 
                                            1
                                            
                                            firm-ripe California avocado
                                            
                                        
- 
                                            1
                                            oz
                                            baby arugula (2 cups) 
                                            
                                        
- 
                                            
                                            
                                            Coarse sea salt to taste (optional)
                                            
                                        
 
                    
                 
            
            
            
            
            
            
            
            
                
                    
                    
                    
                        
                            
                                
                                
                                
                                    
                                        - 
                                            
                                            Plunge lobster headfirst into an 8-quart pot of boiling salted water. Cook, covered, over high heat 6 minutes (for 1 1/4-lb lobster) or 7 minutes (for 1 1/2-lb lobster) from time it enters water. Transfer with tongs to sink to drain. 
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                                            When lobster is cool enough to handle, remove meat from tail and claws, keeping meat intact. Discard tomalley, any roe, and shells. Chill lobster, covered, until cold, at least 1 hour. 
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                                            While lobster chills, stir together shallot, lemon juice, and table salt in a small bowl and let stand at room temperature 30 minutes. Add oil in a stream, whisking. 
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                                            Cut peel, including all white pith, from grapefruit with a sharp knife. Cut segments free from membranes and transfer segments to paper towels to drain. 
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                                            Halve avocado lengthwise, discarding pit. (Save 1 half, wrapped tightly in plastic wrap, for another use.) Halve remaining avocado half lengthwise and peel, then cut crosswise into 1/3-inch-thick slices. 
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                                            Cut lobster tail meat crosswise into 1/2-inch-thick slices. Divide avocado and all of lobster meat between 2 salad plates and arrange grapefruit around them. Top with arugula and drizzle with dressing. Sprinkle lightly with sea salt (if using) and serve immediately. 
 
                        
                    
                    Cooks’ notes: - Lobster can be cooked 1 day ahead and chilled, covered. Slice tail meat just before assembling salad.
- Dressing can be made 1 day ahead and chilled, covered. Whisk well just before drizzling.
- Grapefruit segments can be cut 2 hours ahead and chilled in 1 layer on a paper-towel-lined plate, covered with plastic wrap.
- Avocado can be cut 1 hour ahead and chilled, its surface covered with plastic wrap, on a plate.
- If your sea salt is very coarse, crush it lightly using a mortar and pestle or the bottom of a heavy skillet.
- When salting water for cooking, use 1 tablespoon of salt for every 4 quarts of water.